{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2LTENKRQUDKIXWDZELISCL4ZOI","short_pith_number":"pith:2LTENKRQ","canonical_record":{"source":{"id":"2507.04079","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-07-05T16:03:05Z","cross_cats_sorted":[],"title_canon_sha256":"10e239e5ee0f69193684e2464562cac1402cc5779cdf26fff8a8f4b676fc3f0d","abstract_canon_sha256":"631a44a1661e2d966655413c9192dd2d4caa233dcfd155b49363f816213383a4"},"schema_version":"1.0"},"canonical_sha256":"d2e646aa30a0d48bd87922d1212f99721a8f586fdce5608933b9c5b180dee487","source":{"kind":"arxiv","id":"2507.04079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04079","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04079v1","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04079","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"2LTENKRQUDKI","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"2LTENKRQUDKIXWDZ","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"2LTENKRQ","created_at":"2026-07-05T11:32:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2LTENKRQUDKIXWDZELISCL4ZOI","target":"record","payload":{"canonical_record":{"source":{"id":"2507.04079","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-07-05T16:03:05Z","cross_cats_sorted":[],"title_canon_sha256":"10e239e5ee0f69193684e2464562cac1402cc5779cdf26fff8a8f4b676fc3f0d","abstract_canon_sha256":"631a44a1661e2d966655413c9192dd2d4caa233dcfd155b49363f816213383a4"},"schema_version":"1.0"},"canonical_sha256":"d2e646aa30a0d48bd87922d1212f99721a8f586fdce5608933b9c5b180dee487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:32:41.824809Z","signature_b64":"ieh53eVr89dofgObQplA1eQ//s5buH8WPHiNZMVQI7mQjzJ0MfJyYC4sb8C7oDiywZFwdBNyg6MPTPQkHfxrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2e646aa30a0d48bd87922d1212f99721a8f586fdce5608933b9c5b180dee487","last_reissued_at":"2026-07-05T11:32:41.824297Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:32:41.824297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.04079","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epz/dWJi93uEKLT4Y2C08HT7JfeogWXCAuEj2TH442Kf2aziONLqPnJbQQpZQ6sltiJKGVhSJfsuhTqRdXL+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:54:04.183897Z"},"content_sha256":"7bfdfab87413b8c83bdf5cd3d74fc5d3eb51042527b4d39b4ffb5f415410d4dc","schema_version":"1.0","event_id":"sha256:7bfdfab87413b8c83bdf5cd3d74fc5d3eb51042527b4d39b4ffb5f415410d4dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2LTENKRQUDKIXWDZELISCL4ZOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Growth Rate Analysis in $f(R,L_m)$ Gravity: A Comparative Study with \\boldmath$\\Lambda$CDM Cosmology","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"G. K. Goswami, J. P. Saini","submitted_at":"2025-07-05T16:03:05Z","abstract_excerpt":"We investigate the evolution of cosmic structures within the framework of modified gravity, specifically focusing on theories described by the function $f(R, L_m)$, where $R$ is the Ricci scalar and $L_m$ is the matter Lagrangian. This class of models introduces a non-minimal coupling between geometry and matter, leading to modifications in the dynamics of density perturbations. We derive the linear growth equation and compute the observable growth rate $f\\sigma_8(z)$, which is directly accessible from redshift-space distortion (RSD) data. Using recent observational constraints from galaxy sur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04079","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.04079/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+HNG/33kF0ds8ILzNj7469BH6VST61dqkvl7AtVtrMc1wiFzxkYEC0f9GJQDh2QZwO9LcfMMxkRIWIFofKDdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:54:04.184398Z"},"content_sha256":"b2d8fa963860ac1bb61ae9d269f68e49dcd45a99a912493110c8546095d5590c","schema_version":"1.0","event_id":"sha256:b2d8fa963860ac1bb61ae9d269f68e49dcd45a99a912493110c8546095d5590c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LTENKRQUDKIXWDZELISCL4ZOI/bundle.json","state_url":"https://pith.science/pith/2LTENKRQUDKIXWDZELISCL4ZOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LTENKRQUDKIXWDZELISCL4ZOI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T10:54:04Z","links":{"resolver":"https://pith.science/pith/2LTENKRQUDKIXWDZELISCL4ZOI","bundle":"https://pith.science/pith/2LTENKRQUDKIXWDZELISCL4ZOI/bundle.json","state":"https://pith.science/pith/2LTENKRQUDKIXWDZELISCL4ZOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LTENKRQUDKIXWDZELISCL4ZOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2LTENKRQUDKIXWDZELISCL4ZOI","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"631a44a1661e2d966655413c9192dd2d4caa233dcfd155b49363f816213383a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-07-05T16:03:05Z","title_canon_sha256":"10e239e5ee0f69193684e2464562cac1402cc5779cdf26fff8a8f4b676fc3f0d"},"schema_version":"1.0","source":{"id":"2507.04079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.04079","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2507.04079v1","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.04079","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"2LTENKRQUDKI","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"2LTENKRQUDKIXWDZ","created_at":"2026-07-05T11:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"2LTENKRQ","created_at":"2026-07-05T11:32:41Z"}],"graph_snapshots":[{"event_id":"sha256:b2d8fa963860ac1bb61ae9d269f68e49dcd45a99a912493110c8546095d5590c","target":"graph","created_at":"2026-07-05T11:32:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.04079/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the evolution of cosmic structures within the framework of modified gravity, specifically focusing on theories described by the function $f(R, L_m)$, where $R$ is the Ricci scalar and $L_m$ is the matter Lagrangian. This class of models introduces a non-minimal coupling between geometry and matter, leading to modifications in the dynamics of density perturbations. We derive the linear growth equation and compute the observable growth rate $f\\sigma_8(z)$, which is directly accessible from redshift-space distortion (RSD) data. Using recent observational constraints from galaxy sur","authors_text":"G. K. Goswami, J. P. Saini","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-07-05T16:03:05Z","title":"Growth Rate Analysis in $f(R,L_m)$ Gravity: A Comparative Study with \\boldmath$\\Lambda$CDM Cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.04079","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7bfdfab87413b8c83bdf5cd3d74fc5d3eb51042527b4d39b4ffb5f415410d4dc","target":"record","created_at":"2026-07-05T11:32:41Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"631a44a1661e2d966655413c9192dd2d4caa233dcfd155b49363f816213383a4","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-07-05T16:03:05Z","title_canon_sha256":"10e239e5ee0f69193684e2464562cac1402cc5779cdf26fff8a8f4b676fc3f0d"},"schema_version":"1.0","source":{"id":"2507.04079","kind":"arxiv","version":1}},"canonical_sha256":"d2e646aa30a0d48bd87922d1212f99721a8f586fdce5608933b9c5b180dee487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2e646aa30a0d48bd87922d1212f99721a8f586fdce5608933b9c5b180dee487","first_computed_at":"2026-07-05T11:32:41.824297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:32:41.824297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ieh53eVr89dofgObQplA1eQ//s5buH8WPHiNZMVQI7mQjzJ0MfJyYC4sb8C7oDiywZFwdBNyg6MPTPQkHfxrDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:32:41.824809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.04079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bfdfab87413b8c83bdf5cd3d74fc5d3eb51042527b4d39b4ffb5f415410d4dc","sha256:b2d8fa963860ac1bb61ae9d269f68e49dcd45a99a912493110c8546095d5590c"],"state_sha256":"96beab82f9985b0f14eb585ad0632420d93b137ad1d17f6145f47372f7e9b7a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vxr8cjIN572uqvekMZ5YKYo32Ns2GgcZdVqkDO8Jrue4JYtQaSY9Zvktk9F3YD+8+i4AoVSOAM+ofSie2UNOBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:54:04.189950Z","bundle_sha256":"c0915ca6632b6d37826ead529bbc426200dfe4f61e1df3bb1c4355932a53b026"}}